There was a problem upgrading to Firefox 13. This error kept returning:

/var/cache/apt/archives/firefox_13.0+build1-0ubuntu0.12.04.1_i386.deb
    W: Waited for dpkg --assert-multi-arch but was not there - dpkgGo (10: There are no "child" processes).

Now it seems that there is some problem with dpkg and I can't install anything from software center. I already tried to clean previous packages with sudo rm /var/lib/apt/lists/* -vf and then sudo apt-get update, it didn't work.

When running sudo dpkg --configure -a, I get this:

dpkg: problems with dependencies prevent the configuration of firefox-globalmenu:
firefox-globalmenu depends on firefox (= 13.0+build1-0ubuntu0.12.04.1); however:
  The package is not installed.
dpkg: error while processing firefox-globalmenu (--configure):
problems com dependencies - leaving unconfigured
There has been found errors while processing:
firefox-globalmenu

What should I do to fix this??

EDIT: I don't have the necessary expertise to understand why what I did worked and what was causing the conflict, but anyway, since there was a problem with firefox-globalmenu:, I went to synaptics package manager, I removed this particular package and reinstalled it. After that, I was able to install Firefox from synaptics and also any other applications from software center.

However, still there was a problem, when running sudo apt-get update, the following kept returning:

Failed to get gzip:/var/lib/apt/lists/partial/archive.ubuntu.com_ubuntu_dists_precise_main_binary-i386_Packages  Verification code hash doesn't match.

    E: Some archives index failed at being downloaded. They have been ignored, or older copies are used instead.

So I typed sudo rm /var/lib/apt/lists/* -vf in terminal and then again sudo apt-get update and everything is fine now.

I did this before an answer was posted, anyway I agree the problem was that particular package and its removal. So I'll mark the below answer as accepted.